Question

After school, Maya and Naomi headed to the beach, $6$ miles away. Maya decided to bike while Naomi took a bus. The graph below shows their journeys, indicating the time and distance traveled. What was the difference, in miles per hour, between Naomi's and Maya's average speeds?

$6$

$12$

$18$

$20$

$24$

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Written solution:

Naomi traveled $6$ miles in $10$ minutes. This ratio is $\begin{align*}\dfrac{6 \text{ miles}}{10 \text{ minutes}} &= \dfrac{36 \text{ miles}}{60 \text{ minutes}} \\&= 36 \dfrac{\text{ miles}}{\text{hour}}\end{align*}$

Maya traveled $6$ miles in $30$ minutes. This ratio is $\begin{align*}\dfrac{6 \text{ miles}}{30 \text{ minutes}} &= \dfrac{12 \text{ miles}}{60 \text{ minutes}} \\&= 12 \dfrac{\text{ miles}}{\text{hour}}\end{align*}$

This difference is $36-12=24.$

Thus, the correct answer is E.

2020 AMC 8 Problem 11

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Problem 11 in Other Years